X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;f=octave_packages%2Fm%2Fstatistics%2Ftests%2Fkolmogorov_smirnov_test_2.m;fp=octave_packages%2Fm%2Fstatistics%2Ftests%2Fkolmogorov_smirnov_test_2.m;h=2cadd1c071fb095d6c165273a324c9e8157e3932;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/statistics/tests/kolmogorov_smirnov_test_2.m b/octave_packages/m/statistics/tests/kolmogorov_smirnov_test_2.m new file mode 100644 index 0000000..2cadd1c --- /dev/null +++ b/octave_packages/m/statistics/tests/kolmogorov_smirnov_test_2.m @@ -0,0 +1,104 @@ +## Copyright (C) 1995-2012 Kurt Hornik +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {[@var{pval}, @var{ks}, @var{d}] =} kolmogorov_smirnov_test_2 (@var{x}, @var{y}, @var{alt}) +## Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis +## that the samples @var{x} and @var{y} come from the same (continuous) +## distribution. I.e., if F and G are the CDFs corresponding to the +## @var{x} and @var{y} samples, respectively, then the null is that F == +## G. +## +## With the optional argument string @var{alt}, the alternative of +## interest can be selected. If @var{alt} is @code{"!="} or +## @code{"<>"}, the null is tested against the two-sided alternative F +## != G@. In this case, the test statistic @var{ks} follows a two-sided +## Kolmogorov-Smirnov distribution. If @var{alt} is @code{">"}, the +## one-sided alternative F > G is considered. Similarly for @code{"<"}, +## the one-sided alternative F < G is considered. In this case, the +## test statistic @var{ks} has a one-sided Kolmogorov-Smirnov +## distribution. The default is the two-sided case. +## +## The p-value of the test is returned in @var{pval}. +## +## The third returned value, @var{d}, is the test statistic, the maximum +## vertical distance between the two cumulative distribution functions. +## +## If no output argument is given, the p-value is displayed. +## @end deftypefn + +## Author: KH +## Description: Two-sample Kolmogorov-Smirnov test + +function [pval, ks, d] = kolmogorov_smirnov_test_2 (x, y, alt) + + if (nargin < 2 || nargin > 3) + print_usage (); + endif + + if (! (isvector (x) && isvector (y))) + error ("kolmogorov_smirnov_test_2: both X and Y must be vectors"); + endif + + if (nargin == 2) + alt = "!="; + else + if (! ischar (alt)) + error ("kolmogorov_smirnov_test_2: ALT must be a string"); + endif + endif + + n_x = length (x); + n_y = length (y); + n = n_x * n_y / (n_x + n_y); + x = reshape (x, n_x, 1); + y = reshape (y, n_y, 1); + [s, i] = sort ([x; y]); + count (find (i <= n_x)) = 1 / n_x; + count (find (i > n_x)) = - 1 / n_y; + + z = cumsum (count); + ds = diff (s); + if (any (ds == 0)) + ## There are some ties, so keep only those changes. + warning ("cannot compute correct p-values with ties"); + elems = [find(ds); n_x+n_y]; + z = z(elems); + endif + + if (strcmp (alt, "!=") || strcmp (alt, "<>")) + d = max (abs (z)); + ks = sqrt (n) * d; + pval = 1 - kolmogorov_smirnov_cdf (ks); + elseif (strcmp (alt, ">")) + d = max (z); + ks = sqrt (n) * d; + pval = exp (-2 * ks^2); + elseif (strcmp (alt, "<")) + d = min (z); + ks = -sqrt (n) * d; + pval = exp (-2 * ks^2); + else + error ("kolmogorov_smirnov_test_2: option %s not recognized", alt); + endif + + if (nargout == 0) + printf (" pval: %g\n", pval); + endif + +endfunction